Mac 1105 Final Review With Complete Verified Solutions

MAC 1105 FINAL REVIEW WITH COMPLETE VERIFIED SOLUTIONS Distance formula - RIGHT ANSWER -Square root ((x2-x1)^2+(y2-y1)^2) even function - RIGHT ANSWER -f (x)=f (-x) Formula of a circle at the origin - RIGHT ANSWER -X^2+y^2=r^2 Formula of a circle whose center is not at the origin (h, k) - RIGHT ANSWER -(X-h)^2 + (y-k)^2=r^2 HA's - RIGHT ANSWER -Same degree:leading coefficient over leading coefficient, larger on top: doesn't exist, larger on bottom:0 Horizontal shifts Y=f (x+c) Y=f (x-c) - RIGHT ANSWER -To the left by c units To the left by c units Horizontal stretch and shrink Y=f (cx), c 1 Y=f (cx), 0c 1 - RIGHT ANSWER -Divide each c coordinate by x- horizontally shrinking Divide each c coordinate by x- horizontally stretching How to find an algebraic inverse - RIGHT ANSWER -1. Replace f (x) with y 2. Swap x and y for y ce y with f^-1 (x) I^2 - RIGHT ANSWER --1 Logs have what kind of asymptotes? - RIGHT ANSWER -VA's Midpoint formula - RIGHT ANSWER -(X2-x1 /2, y2-y1/2) Odd function - RIGHT ANSWER -f (-x)= -f (x) Order of graphing transformations - RIGHT ANSWER -1. Horizontal shifts 2. Horizontal stretches and shrinks 3. Vertical stretches or shrinks 4. Reflections 5. Vertical shifts Reflections Y=-f (x) Y=f (-x) - RIGHT ANSWER -Reflects about x axis Reflects about Y axis Standard form of a line - RIGHT ANSWER -Ax+by=c Vertex in vertex form - RIGHT ANSWER -(H, k) Vertex NOT in vertex form - RIGHT ANSWER -V=-b/2a for the x coordinate, f (-b/2a) for u coordinate Vertical shifts Y=f (x)+c Y=f (x)-c - RIGHT ANSWER -Goes up by c units Goes down by c units Vertical stretch and shrink Y=cf (x), c 1 Y=cf (x), 0 c 1 - RIGHT ANSWER -Multiply Y coordinates by c- vertical stretch Multiply each Y coordinates by c- vertical shrinking